Measuring the $^{127}$I, $\nu_{e}$ Charged-Current Cross-Section of NaI[Tl]

The primary objective of this experiment is to measure the cross-section of $\nu_{e}$ charged-current neutrino interactions on $^{127}$I. To measure this interaction, an array of twenty-four, 7.7 kg sodium iodide (NaI[Tl]) scintillating detectors will be deployed to the Spallation Neutron Source at Oak Ridge National Laboratory. The design of the detector array is presented here along with preliminary characterization and background measurements conducted at Duke University.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.